A conventional radar derives the range of a target from a measurement of the round-trip time of a signal. This method works if the transmission medium produces negligible signal distortions. This condition is typically satisfied if the transmission medium is the atmosphere, empty space, dry ground, solid rock, ice, or the like. There are other transmission media that produce such large signal distortions that the measurement of range based on round-trip time fails. Typical examples are media containing water, ranging from minerals with low water content at one extreme to water with low mineral content at the other extreme; another example is hot or molten rock at great depths of the Earth. In these cases, one can still obtain range information of scattering or reflecting objects by observing the distortions of the returned signal.
The measurement of range or distance of scattering or reflecting objects by means of the radar principle discussed above has been known for more than eighty years. The round trip time .DELTA.T of an electromagnetic signal returned by a scattering or reflecting object is observed and the range d=c.DELTA.T/2 is derived from velocity of light c=1/.sqroot..epsilon..mu., where .epsilon. and .mu. are the permittivity and the permeability of the medium. This approach works as long as the conductivity .sigma. of the medium can be ignored, which is the case in vacuum, the atmosphere, dry soil or rock, etc. If significant amounts of water are present or if electromagnetic signals are used to probe hot or molten rock, the conductivity .sigma. can no longer be ignored. Signals transmitted through such a medium are significantly distorted, which makes the definition of a round trip time .DELTA.T difficult, and the propagation velocity of the signals is no longer defined by c=1/.sqroot..epsilon..mu.. Hence range determination by means of the conventional radar principle is no longer possible.
In order to overcome this difficulty, one must study the propagation of electromagnetic signals in lossy media. This study ran into an unexpected obstacle. It was found that Maxwell's equations, which are the basis for electromagnetic wave transmission, fail for the propagation of pulses or "transients" in lossy media. The reason turned out to be the lack of a magnetic current density term analogous to the electric current density term. Such a magnetic current density term does not occur in Maxwell's equations because magnetic charges equivalent to negative electric charges (electrons, negative ions) or to positive electric charges (positrons, protons, positive ions) have not been observed reliably. However, currents are not only carried by charges but also by dipoles or higher order multipoles. For instance, the electric current flowing through the dielectric of a capacitor is carried by electric dipoles, which is the reason why the "polarization" current in a capacitor is different from the current in a resistor that is carried by charges or monopoles. Since magnetic dipoles are known to exist, the magnetic compass needle being such a dipole, there must be magnetic polarization currents carried by these dipoles, and this fact calls for a magnetic density term in Maxwell's equations; the existence of magnetic charges or monopoles is neither implied nor denied by such a term.
The modification of Maxwell's equations and the transient solutions derived from the modified equations are discussed in H. F. Harmuth, Propagation of Nonsinusoidal Electromagnetic Waves, Academic Press, New York 1986, which is hereby incorporated by reference. Using these solutions, the propagation and distortion of electromagnetic signals was further studied in the PhD thesis "Propagation velocity of electromagnetic signals in lossy media in the presence of noise", by R. N. Boules, Department of Electrical Engineering, The Catholic University of America, Washington D.C., 1989. This thesis contains computer plots of distorted signals having propagated in lossy media with a certain conductivity .sigma. over various distances. In particular, the case .sigma.=4 S/m, relative permittivity 80, and relative permeability 1--which are typical values for sea water--is treated in some detail.